Mathematical Analysis of Casson Fluid Model for Blood Rheology in Stenosed Narrow Arteries

Abstract

The flow of blood through a narrow artery with bell-shaped stenosis is investigated, treating blood as Casson fluid. Present results are compared with the results of the Herschel-Bulkley fluid model obtained by Misra and Shit (2006) for the same geometry. Resistance to flow and skin friction are normalized in two different ways such as (i) with respect to the same non-Newtonian fluid in a normal artery which gives the effect of a stenosis and (ii) with respect to the Newtonian fluid in the stenosed artery which spells out the non-Newtonian effects of the fluid. It is found that the resistance to flow and skin friction increase with the increase of maximum depth of the stenosis, but these flow quantities (when normalized with non-Newtonian fluid in normal artery) decrease with the increase of the yield stress, as obtained by Misra and Shit (2006). It is also noticed that the resistance to flow and skin friction increase (when normalized with Newtonian fluid in stenosed artery) with the increase of the yield stress.